Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
330 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10592606 | C2 | semidirect |
| 3. #10590622 | C2 | semidirect |
| 4. C3×#4515 | C2 | semidirect |
| 5. C3×#4511 | C2 | semidirect |
| 6. #10589113 | C2 | semidirect |
| 7. #10589103 | C2 | semidirect |
| 35. #4515 | D3 | semidirect |
| 36. #4511 | D3 | semidirect |
| 275. C32 | #2171 | semidirect |
| 312. C3 | #69123 | semidirect |
| 313. C3 | #69301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592606 | 2 |
| #10590923 | 2 |
| #10590622 | 2 |
| C3×#4515 | 2 |
| C3×#4511 | 2 |
| #10589113 | 2 |
| #10589103 | 2 |
| #69301 | 3 |
| #69123 | 3 |